1. Field of the Invention
This invention relates to a method and apparatus for passive localisation of a source that emits a signal, and particularly but not exclusively for passive localisation of a radar or radio transmitter.
2. Discussion of Prior Art
The best known method for passive localisation of a signal emitting source is based on determining a bearing line, or direction of arrival, from each of several non-collocated sensors dispersed over some surveillance area of interest. When there are no measurement errors, all bearing lines will intersect at one point representing the source location. In practice, errors are always present and the source location is estimated by exploiting one of the many algorithms developed during the last sixty years.
Other known methods to localise a signal emitting source exploit various relationships between parameters of signal replicas received at different suitably positioned sensors. For example, when the speed of signal propagation is known, it is possible to localise a source by determining the relative delays between signals intercepted by several sensors whose positions are known. In some cases it is also possible to determine the source location by utilizing information contained in the phase of signals received by non-collocated sensors with known positions. When there is some relative movement between a source and sensors, the signal phase varies in time to produce the well-known Doppler effect. An example of such a method is described in U.S. Pat. No. 4,385,301.
The problem with the above techniques is that there are a number of applications where neither of the above methods can be used. Another method applies the concept of the circle of Apollonius. The power received at each energy detector is determined. The locus of a point X is determined whose distance from two of said sensors satisfy the equation P1/P2=d22/d12 where P1 and P2 are respectively the power received at sensors 1 and 2 respectively and d2 and d1 are the distances of the points on the locus from sensors 2 and 1 respectively. The locus of a point Y is determined whose distance from two of said sensors satisfy the equation P3/P2=d22/d32 where P3 and P2 are respectively the power received at sensors 3 and 2 respectively and d2 and d3 are the distances of the points on the locus from sensors 2 and 3 respectively. The intersect of said loci is where the power source is located. Three different ratios of power values measured by the sensors S1, S2 and S3 determine three circles. The source is located at the point where the three circles intersect. This is shown in FIG. 1 and described in U.S. Pat. No. 4,494,119.
A straightforward application of the concept of circle of Apollonius to source localisation problems is difficult for a number of reasons. When the number of power measurements is equal to N, the number of all possible ratios of two powers is equal to N(Nxe2x88x921)/2. Since the number of independent power measurements is only N, all the N(Nxe2x88x921)/2 ratios cannot provide independent information. Therefore, a localisation algorithm based on ratios of only two powers cannot be computationally efficient. In some ESM applications a single moving sensor can provide more than 1000 power measurementswhich will define almost half a million circles. Additionally, the location estimate is derived from the geometrical construction of a circle of Apollonius. Therefore, any attempt to find a maximum likelihood or Bayesian estimate of location will have to be based on advanced concepts of stochastic geometry and geometric probability. The solution may be too difficult to implement with a hardware digital processor.
The inventor has determined that all measured (also called direct) powers can be used in each ratio to determine the location of a source. In order to mitigate the problems with the prior art, in this invention, when the number of power measurements made at different sensor positions is N, the number of ratios of power employed for localisation is equal to Nxe2x88x921, and exactly all powers appear in each such ratio.
The invention also enables the localisation of a signal emitting source by suitable processing of intercepted signals which may have been corrupted by noise and other interference.
The invention comprises a method of locating a signal emitting source comprising the steps of:
a) making measurements of power received from the source by a set of sensors and selecting N such measurements from respective sensors, where N is an even number and at least four;
b) constructing Nxe2x88x921 direct power ratios each derived from the N power measurements, each ratio having a numerator which is the product of a respective sub-set of N/2 of the N power measurements and a denominator which is the product of the N/2 outside such sub-set in each case; and; and
c) calculating the source location from the direct power ratios.
Preferably, the location of the signal emitting source is calculated by comparing the direct power ratios with the respective ratios predicted for each of a plurality of hypothesized source locations. The signal emitting source is calculated by:
a) calculating predicted power ratios for each of a plurality of hypothesized source locations;
b) comparing the direct power ratios with the predicted power ratios; and identifying the hypothesized source location having the smallest discrepancy between the predicted power ratios and the direct power ratios. An estimated source location is such a hypothesized location where a suitably defined measure of discrepancy between the measured and predicted ratios achieves a minimum value.
The combinatorial problem of identifying and forming all the ratios is preferably facilitated by the use of a suitably constructed Hadamard matrix.
Preferably, each direct power ratio is converted with a logarithmic transformation into a linear combination of measured powers. The logarithmic transformation converts the products into sums and the ratios into differences. The Hadamard transformation facilitates the combinatorial problem of constructing a complete set of direct power ratios by exploiting the properties of the Hadamard Transform. Furthermore, the logarithmic transformation converts direct power ratios into random variables with approximately Gaussian distribution, irrespective of the nature of intercepted signals.
Preferably, the measure of discrepancy between measured (or direct) and predicted power ratios utilizes the absolute difference between the logarithms of the respective ratios.
The invention may preferably be utilised in conjunction with standard electronic support measure (ESM) system which provides bearing estimates but also using available information about the power of intercepted signals for localisation purposes. Incorporating this information in an appropriate manner into the localisation algorithm will result in a significant reduction of localisation errors. Similar performance enhancement can also be achieved, at least in some cases, in other applications (e.g., surveillance or xe2x80x98search and rescuexe2x80x99 missions) concerning localisation and tracking of communication transmitters (e.g., mobile phones) with the use of compact power sensors.